Abstract
To effectively improve the accuracy of attitude reconstruction under highly dynamic environments, a new numerical attitude updating algorithm is designed in this paper based on the high-order polynomial iteration according to the differential equation for quaternion. In this algorithm, a high-order polynomial is introduced to fit the angular rate accurately without increasing the number of gyro outputs during per attitude updating interval. This algorithm can provide an exact high-order polynomial solution for quaternion and the process of attitude reconstruction can be implemented efficiently. The algorithm’s performance is evaluated as compared with optimal coning algorithm, attitude quaternion updating algorithm based on Picard iteration (QPI), and higher-order rotation vector attitude updating algorithm (Fourth4Rot) under coning motion. The simulation results show that this algorithm can improve the accuracy of attitude computation and clearly outperform the optimal coning algorithm, QPI, and Fourth4Rot in high dynamic environment.
Highlights
Unlike gimbaled inertial navigation system (GINS), strapdown inertial navigation system (SINS) uses a digital platform as an inertial navigation platform, in which the attitude matrix is applied to describe the orientation of the digital platform with respect to the body coordinate frame [1]
SIMULATION RESULTS AND DISCUSSION the simulated classical coning motion data is used to evaluate the convergence of the new algorithm and the performance of the new algorithm (New) as compared with the optimal coning algorithm (Optimal), QPI, and Fourth4Rot
Where ql (Nh, 0) is the updating quaternion which equals to the sum of the first l + 1 terms in (39) and el is a 4 dimension vector
Summary
Unlike gimbaled inertial navigation system (GINS), strapdown inertial navigation system (SINS) uses a digital platform as an inertial navigation platform, in which the attitude matrix is applied to describe the orientation of the digital platform with respect to the body coordinate frame [1]. X. Liu et al.: Accurate Numerical Algorithm for Attitude Updating Based on High-Order Polynomial Iteration frequency range [8]. The above mentioned attitude updating algorithms mainly calculate the non-commutability error compensation terms directly or indirectly based on polynomial motion model or coning motion model. This paper presents an accurate numerical method for quaternion differential equation based on the combination of the high-order polynomial model and QPI, in which the polynomial fitting order is increased to N or N + 1 up from N − 1. In this algorithm, the exact polynomial solution for the quaternion can be iteratively obtained. The cross product terms on the same dotted oblique line, more constraints could be introduced to determine parameters cN , cN+1, · · · , and ck
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